The present invention comprises a new and distinct dogwood cultivar hereinafter referred to by the cultivar name ‘NCCE1’. This new dogwood was developed through a breeding program in Mills River, N.C. ‘NCCE1’ was selected from a population of seedlings grown from an open-pollinated Cornus elliptica ‘Elsbry’, NCSU 2006-030 (U.S. Plant Pat. No. 14,537). The first asexual propagation of ‘NCCE1’ was carried out in July 2010 by rooting stem cuttings in Mills River, N.C. and has been asexually reproduced repeatedly by vegetative cuttings and micropropagation from axillary shoots over a 5-year period. ‘NCCE1’ roots readily from softwood cuttings treated with a basal dip of 4,000-5,000 ppm indole butyric acid (potassium salt) in water. ‘NCCE1’ has been found to retain its distinctive characteristics through successive asexual propagations.